Adds the high-powered attorney: “He will have a meaningful relationship with Suri.”

As for when Cruise will see his daughter, who has been clocking in time with her mom in New York – from trips to the zoo to the art museum – Fields could not reveal a specific time or date. (Cruise is currently filmingOblivion.)

“I don’t know the details of his schedule, so I can’t comment,” he says. “My guess is he’ll be seeing Suri very soon.”

Regarding the role the actor’s religion played in the settlement, Fields tells PEOPLE, “Somebody said the Scientologists were directing the negotiations, and that is absolute hogwash. There was no Scientologist present, I wasn’t on the phone with Scientologists. Scientologists played no part of role in the negotiations between the lawyers.”

Instead, he says, both teams “dealt rationally with the issues, hashed them all out and over a few days worked something out that was to the satisfaction of both sides.”